Lemma 2.1 ([1]}) 
Suppose that A is linear bounded operator defined on the Banach space \(X\)  and assume that \(\Vert A\Vert  < 1\) . Then, \((I-A)^{-1}\)  is linear bounded on \(X\)  and
\((I-A)^{-1}=\sum _{k=0}^{\infty }A^{k}.\) 

